Multis tiscale cale modelling lling of CMS electric ctrical al breakdown kdown at high h electric ctric field HIP Flyura Djurabekova, Helga Timkó, Aarne Pohjonen, Stefan Parviainen, Leila Costelle and Kai Nordlund Helsinki Institute of Physics and Department of Physics University of Helsinki Finland
Arcing occurs in fusion reactors: in regions in direct contact with the plasma such as the divertor in region not in direct contact with the plasma such as the limiters Arc is a significant source of erosion of first wall material and has even been reported to remove limiter coating layers entirely! Matter flying from the wall into the plasma in an arc can disrupt the normal operation Flyura Djurabekova, HIP, University of Helsinki 4
Flyura Djurabekova, HIP, University of Helsinki 5
R. Behrisch, , Plenum, 1986 Stage 1: Charge distribut ution n @ surface ~few fs Metho hod: DFT with externa nal electric field Stage 2: Atomic motion n & evaporation n + + ~few ns Joul ule heating ng (electron n dynamics) Metho hod: Hybrid ED&MD model (includ udes Laplace e and heat equation solutions) ~ sec/min ~ sec/hours Stage e 3a: Onset of tip growth; h; Stage 3b: Evolut ution of surface Dislocation n mecha hanism morpho hology y due to the given charge distribut ution n Metho hod: MD, Molecular Statics… Method hod: Kinetic Monte e Carlo ~10s ns Stage 4: Plasma evolut ution, n, burning of arc Metho hod: Particle-in in-Cell (PIC) ~100s ns Stage 5: Surface damage due to the intens nse ion bombardment ent from plasma Metho hod: Arc MD Flyura Djurabekova, HIP, University of Helsinki 6
In our group we use all main atomic-level simulation methods: Density functional theory (DFT) Solving Schrödinger equation to get electronic structure of atomic system Molecular dynamics (MD) Simulation of atom motion, classically and by DFT Kinetic Monte Carlo (KMC) Simulation of atom or defect migration in time Simulations of plasma-wall interactions Simulation of plasma particle interactions with surfaces We use all of them to tackle the arcing effects! Flyura Djurabekova, HIP, University of Helsinki 7
Macroscopic field to… Gauss law by ’ pllbox ’ technique Q surface E 0 A surface Due to the external electr tric field d the surface e attains charge ge …the atomic level: Two electric forces modify the motion of charged atoms: 0.01 1 GV E m F Eq F F F L coulomb coulomb coulomb + F F F F F F a a a b b b + + + 1 q q a i F r a a a + b + b + b + b + + + C 0i 2 4 r i 0 0i F F F F F F b b b a a a Flyura Djurabekova, HIP, University of Helsinki 8
Solut ution n of 3d Laplace ce equation n for the surfa face ce with h the tip of 20 atomi mic c layer ers, s, mixed ed bounda undary y condit dition n (color represent esents s the charges) es) 2 0 Flyura Djurabekova, HIP, University of Helsinki 9
Atom/cluste cluster r evaporat atio ion n from Cu(100) @ 500 K, E 0 1 GV/m Flyura Djurabekova, HIP, University of Helsinki 10
Follow evolution of the surfaces by calculating the partial charge induced on metal surface atoms The dynamics of atom charges follows the shape of electric field distortion on tips on the surface Temperature of the surface is sufficient, atom evaporation enhanced by the field can supply neutrals to build up the F. F. Djurabek ekova va, S. Parvi viainen nen, A. Pohjonen nen and K. Nordlund und, , PRE 83, 026704 (2011). plasma densities above surface. Flyura Djurabekova, HIP, University of Helsinki 11
DFT details: Code: SIESTA For exchange and correlations functionals the Perdew, Burke and Ernzerhof scheme of Generalized gradient approximation (GGA) Slab organized in 8 layers+ 8 E o =-1 GV/m layers of vacuum External field is added to calculate the electrostatic potential in the vacuum Q surf 16 16 e e E 5.53 10 5.49 10 0 2 2 m m A surf Flyura Djurabekova, HIP, University of Helsinki 12
We have calculated the workfunction for Cu surface when a single adatom is present E W E F s V W S E V Flyura Djurabekova, HIP, University of Helsinki 13
Every atomic column produces the current dependent on the field above the column. The current from the tip is an average over all the columns. ( , , ) ( , , ) ( , ) J E T E T J E T 0 J e 2 3/2 aE b E 0 J 0 ( , ) E exp E E i k T d / ( , ) E B T ( , , ) E T T sin k T / d ( , ) E B T Fowler- Nordheim 2 constants: A V e a 1.541 2 8 h eV P 8 2 V m b 6.831 3/2 3 eV nm eh P Flyura Djurabekova, HIP, University of Helsinki 14
The heat conduction from the tip has been implemented into PARCAS by solving the heat conduction equation 2 T x t ( , ) 1 T x t ( , ) 2 T x t ( , ) J x ( ) K T ( ) e 2 t C x V T, K T, K Here C V volumetric heat capacity. Phonons are implicitly present in classical MD . In the equation we include J el (x) J(x) only electron thermal conductivity given by the Wiedemann- Franz law LT ( ) K T e ( ) T Where Lorenz number is found as 2 2 8 -2 L ( /3)( k ) 2.443 10 W K B S. Parviainen, F. Djurabekova, H. Timko, and K. Nordlund, Comput ut. Mater. Sci. 50, 2075 (2011). Flyura Djurabekova, HIP, University of Helsinki 15
The dislocation motion is strongly bound to the atomic structure of metals. In FCC (face-centered cubic) the dislocation are the most mobile and HCP (hexagonal close-packed) are the hardest for dislocation mobility. Flyura Djurabekova, HIP, University of Helsinki 16
We simulated a void near {110} Cu surface , when the high tensile stress is applied on the surface. Bottom is fixed, lateral boundary allowed to move in z direction. A. Pohjonen, F. Djurabekova, et al., Dislocation nucleation from near surface void under static tensile stress on surface in Cu, Jour. Appl. Phys. 110, 023509 (2011). Flyura Djurabekova, HIP, University of Helsinki 17
Half-void of diameter 4nm in {110} Cu surface. (N of atoms 1 70000 atoms…) E0=22 GV/m (exaggeration is required to simulate the dislocation within the MD time span) T = 600 K Flyura Djurabekova, HIP, University of Helsinki 18
A screw dislocation placed so that it intersects the void on a side, showed a cross-slip behavior leading to the atom step on the surface. This mechanism eventually combines with the previous mechanism, but to ignite this process less stress is required (in our simulations 1.7 GPa against 3 GPa). Flyura Djurabekova, HIP, University of Helsinki 19
In real life we can observe the full dynamic range of a vacuum discharge: Up to 12 orders ude of magnitud > 10s pA in ‘weak’ FE phase nce differenc Space charge limited ‘strong’ FE phase, typically ~ nA – μ A Discharge current, up to 10 – 100 A At the same time, the involved area changes: Up to 12 orders ude Typically 10 -20 – 10 -14 m 2 for weak FE R em ~ 0.1 – 100 nm of magnitud nce differenc During the discharge, the bombarded area has R ~ 10 – 100 μ m 10s μ m Discharge ge Cu Cu + e e - - FE FE 10s nm Flyura Djurabekova, HIP, University of Helsinki 20
Corres espond nding to experi erimen ent... .. Up Up to to now we we have electros rosta tatic tic PIC PIC-MCC codes: 1d3v j FE the 2D-model Provide de us with a link betwe ween 1. Micro- & macroscopic surface processes: Triggering (nano-scale) plasma crater formation (visible effect) 2. Theory & experiments: Using reasonable physical assumptions (theory), the aim is to predict the evolution of measurable quantities (experiment) H. Timko, K. Matyash, R. Schneider, F. Djurabekova, K. Nordlund, A. Hansen, A. Descoeudres, J. Kovermann, A. Grudiev, W. Wuensch, S. Calatroni, and M. Taborelli , Contrib. Plasma Phys. 5 1, 5-21 (2011) Flyura Djurabekova, HIP, University of Helsinki 21
Flyura Djurabekova, HIP, University of Helsinki 22
0.96 ns Fully cathode dominated phenomenon Although FE starts from a small area, the discharge plasma can involve a macroscopic area on the cathode Transitions seen: 1. Transition from strong FE to a small discharge plasma 1.06 ns 1. - Sudden ionisation avalanche - A plasma sheath forms, the plasma becomes quasi- neutral - Focusing effect Transition from a surface-defined phase to a volume- 2. defined phase 2. 1.60 ns - When neutrals fill the whole system - Self-maintaining - Macroscopic damage Flyura Djurabekova, HIP, University of Helsinki 23
Huge fluxes s of accele lerat rated ed ions are the reaso son n for surfac ace damage Ion fluxes leave rims of peculiar shape Flyura Djurabekova, HIP, University of Helsinki 24
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